Question: Simplify the following expression: $ t = \dfrac{-7}{4} + \dfrac{-k - 9}{-3k} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-3k}{-3k}$ $ \dfrac{-7}{4} \times \dfrac{-3k}{-3k} = \dfrac{21k}{-12k} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-k - 9}{-3k} \times \dfrac{4}{4} = \dfrac{-4k - 36}{-12k} $ Therefore $ t = \dfrac{21k}{-12k} + \dfrac{-4k - 36}{-12k} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{21k - 4k - 36}{-12k} $ $t = \dfrac{17k - 36}{-12k}$ Simplify the expression by dividing the numerator and denominator by -1: $t = \dfrac{-17k + 36}{12k}$